This snippet from the logrotate manpage should explain whats going on:

weekly Log files are rotated if the current weekday is
less then the weekday of the last rotation or if
more then a week has passed since the last rota-
tion. This is normally the same as rotating logs on
the first day of the week, but it works better if
logrotate is not run every night.

What I would do is add that snippet above into a file /etc/logrotate.d/ called http, web or whatever you want.

Because the line "include /etc/logrotate.d" points to a directory logrotate will include all files in that directory and because your "daily" option is specific to those log files it will override the global "weekly" option.

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Basically, what you suggest (the daily modification) would do what you want. Separating the different "domains"(:-) of httpd logs into separate logrotate.d files (as AlanBell suggests) would be nicem since then you'd be able to retain the "slow rotation" of the main service logs. Or running webalizer from a separate cronjob (as Kubrik suggests) would also work nicely (keeping both main logs and mydomain.com logs at "weekly" rotations).
But as said, you'd be fine with the "daily". (I'm buting in, since I suggested logrotate to nova2002 in http://www.experts-exchange.com/Operating_Systems/Linux/Q_20780811.html ...)

I have been scripting applications way too long and can never remember how to create an ISS file. So I decided to write this article to act as my own knowledge base for future reference, and hope you will also benefit.
An ISS file is a response …

Learn how to navigate the file tree with the shell.
Use pwd to print the current working directory: Use ls to list a directory's contents: Use cd to change to a new directory: Use wildcards instead of typing out long directory names: Use ../ to move…